1. Capital-Budgeting
Techniques

2. Capital Budgeting Concepts
Capital Budgeting involves evaluation of (and decision about) projects. Which projects should be accepted? Here, our goal is to accept a project which maximizes the shareholder wealth. Benefits are worth more than the cost.
The Capital Budgeting is based on forecasting.
Estimate future expected cash flows.
Evaluate project based on the evaluation method.
Classification of Projects
Mutually Exclusive - accept ONE project only
Independent - accept ALL profitable projects.

3. Capital Budgeting Concepts
Cash Flows
Initial Cash Outlay - amount of capital spent to get project going.

4. Capital Budgeting Concepts
Cash Flows
Initial Cash Outlay - amount of capital spent to get project going.
If spend $10 million to build new plant then the Initial Outlay (IO) = $10 million
CF0 = Cash Flow time 0 = -10 million

5. Capital Budgeting Concepts
Cash Flows
Initial Cash Outlay - amount of capital spent to get project going.
If spend $10 million to build new plant then the Initial Outlay (IO) = $10 million
CF0 = Cash Flow time 0 = -10 million
Annual Cash Inflows--after-tax CF
Cash inflows from the project
CFn = Sales - Costs
We will determine these in Chapter 10

6. Capital Budgeting Methods
Payback Period
Number of years needed to recover your initial outlay.

7. Capital Budgeting Methods
Payback Period
Number of years needed to recover your initial outlay.
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000

8. Capital Budgeting Methods
Payback Period
Number of years needed to recover your initial outlay.
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
(10,000)
3,500
3,500
3,500
3,500

9. Capital Budgeting Methods
Payback Period
Number of years needed to recover your initial outlay.
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
(10,000)
3,500
-6,500
3,500
3,500
3,500
Cumulative CF

10. Capital Budgeting Methods
Payback Period
Number of years needed to recover your initial outlay.
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
(10,000)
3,500
-6,500
3,500
-3,000
3,500
3,500
Cumulative CF

11. Capital Budgeting Methods
Payback Period
Number of years needed to recover your initial outlay.
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
(10,000)
3,500
-6,500
3,500
-3,000
3,500
+500
3,500
Cumulative CF

12. Capital Budgeting Methods
Payback Period
Number of years needed to recover your initial outlay.
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
(10,000)
3,500
-6,500
3,500
-3,000
3,500
+500
3,500
Cumulative CF
Payback 2.86 years

13. Capital Budgeting Methods
Payback Period
Number of years needed to recover your initial outlay.
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000

14. Capital Budgeting Methods
Payback Period
Number of years needed to recover your initial outlay.
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
(10,000)
500
500
4,600
10,000

15. Capital Budgeting Methods
Payback Period
Number of years needed to recover your initial outlay.
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
(10,000)
500
-9,500
500
4,600
10,000
Cumulative CF

16. Capital Budgeting Methods
Payback Period
Number of years needed to recover your initial outlay.
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
(10,000)
500
-9,500
500
-9,000
4,600
10,000
Cumulative CF

17. Capital Budgeting Methods
Payback Period
Number of years needed to recover your initial outlay.
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
(10,000)
500
-9,500
500
-9,000
4,600
-4,400
10,000
Cumulative CF

18. Capital Budgeting Methods
Payback Period
Number of years needed to recover your initial outlay.
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
(10,000)
500
-9,500
500
-9,000
4,600
-4,400
10,000
+5,600
Cumulative CF

19. Capital Budgeting Methods
Payback Period
Number of years needed to recover your initial outlay.
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
(10,000)
500
-9,500
500
-9,000
4,600
-4,400
10,000
+5,600
Cumulative CF
Payback = 3.44 years

20. Capital Budgeting Methods
Payback Period
Number of years needed to recover your initial outlay.
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
Evaluation:
Company sets maximum acceptable payback. If Max PB = 3 years, accept project A and reject project C
(10,000)
500
-9,500
500
-9,000
4,600
-4,400
10,000
+5,600
Cumulative CF
Payback 3.44 years

21. Payback Method
The payback method is not a good method as it does not consider the time value of money.
Which project should you choose?
CF CF CF CF3
A , , , ,000
B -100, , , ,000

22. Payback Method
The Discounted payback method can correct this shortcoming of the payback method.
To find the discounted pay back
(1) Find the PV of each cash flow on the time line.
(2) Find the payback using the discounted CF and NOT the CF.
Example In Table 9-2

23. Payback Method
Also, the payback method is not a good method as it does not consider the cash flows beyond the payback period.

24. Payback Method
Also, the payback method is not a good method as it does not consider the cash flows beyond the payback period.
Which project should you choose?
CF CF CF Cf CF4 A B

25. Payback Method
Also, the payback method is not a good method as it does not consider the cash flows beyond the payback period.
Which project should you choose?
CF CF CF Cf CF4
A , , ,
B , , , , ,0000
These two shortcomings often result in an incorrect decisions.

26. Capital Budgeting Methods
Methods that consider time value of money and all cash flows
Net Present Value:
Present Value of all costs and benefits of a project.

27. Capital Budgeting Methods
Net Present Value
Present Value of all costs and benefits of a project.
Concept is similar to Intrinsic Value of a security but subtracts cost of the project.
NPV = PV of Inflows - Initial Outlay

28. Capital Budgeting Methods
Net Present Value
Present Value of all costs and benefits of a project.
Concept is similar to Intrinsic Value of a security but subtracts of cost of project.
NPV = PV of Inflows - Initial Outlay
CF1
(1+ k )
CF2
(1+ k )2
CF3
(1+ k )3
CFn
(1+ k )n
NPV = ··· – IO

29. Capital Budgeting Methods
Net Present Value
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
k=10%
(10,000)
500
500
4,600
10,000

30. Capital Budgeting Methods
Net Present Value
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
k=10%
(10,000)
500
500
4,600
10,000
$500
(1.10)
455

31. Capital Budgeting Methods
Net Present Value
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
k=10%
(10,000)
500
500
4,600
10,000
$500
(1.10) 2
455
413

32. Capital Budgeting Methods
Net Present Value
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
k=10%
(10,000)
500
500
4,600
10,000
455
$4,600
(1.10) 3
413
3,456

33. Capital Budgeting Methods
Net Present Value
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
k=10%
(10,000)
500
500
4,600
10,000
455
413
$10,000
(1.10) 4
3,456
6,830

34. Capital Budgeting Methods
Net Present Value
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
k=10%
(10,000)
500
500
4,600
10,000
455
413
3,456
6,830
$11,154

35. Capital Budgeting Methods
Net Present Value
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
k=10%
(10,000)
500
500
4,600
10,000
455
PV Benefits > PV Costs
413
$11,154 > $ 10,000
3,456
6,830
$11,154

36. Capital Budgeting Methods
Net Present Value
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
k=10%
(10,000)
500
500
4,600
10,000
455
PV Benefits > PV Costs
NPV > $0
413
$11,154 > $ 10,000
$1,154 > $0
3,456
6,830
$11,154
$1,154 = NPV

37. Capital Budgeting Methods
Net Present Value
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
k=10%
(10,000)
3,500
3,500
3,500
3,500

38. Capital Budgeting Methods
Net Present Value
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
k=10%
(10,000)
3,500
3,500
3,500
3,500
3,500
(1+ .1 )
3,500
(1+ .1)2
3,500
(1+ .1 )3
3,500
(1+ .1 )4
NPV = – 10,000

39. Capital Budgeting Methods
Net Present Value
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
k=10%
(10,000)
3,500
3,500
3,500
3,500
3,500
(1+ .1 )
3,500
(1+ .1)2
3,500
(1+ .1 )3
3,500
(1+ .1 )4
NPV = – 10,000
PV of 3,500 Annuity for 4 years at 10%

40. Capital Budgeting Methods
Net Present Value
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
k=10%
(10,000)
3,500
3,500
3,500
3,500
3,500
(1+ .1 )
3,500
(1+ .1)2
3,500
(1+ .1 )3
3,500
(1+ .1 )4
NPV = – 10,000
= 3,500 x PVIFA 4, ,000
= 11,095 – 10,000 = $1,095

41. Capital Budgeting Methods
NPV Decision Rules
If projects are independent then accept all projects with NPV ³ 0.
ACCEPT A & B

42. Capital Budgeting Methods
NPV Decision Rules
If projects are independent then accept all projects with NPV ³ 0.
If projects are mutually exclusive, accept projects with higher NPV.
ACCEPT A & B
ACCEPT B only

43. Net Present Value Profile
Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
3,500
(1+ 0 )
3,500
(1+ 0)2
3,500
(1+ 0 )3
3,500
(1+ 0)4
NPV(0%) = – 10,000
= $4,000

44. Net Present Value Profile
Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
3,500
( )
3,500
(1+ .05)2
3,500
( )3
3,500
(1+ .05)4
NPV(5%) = – 10,000
= $2,411

45. Net Present Value Profile
Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
3,500
( )
3,500
(1+ .10)2
3,500
( )3
3,500
(1+ .10)4
NPV(10%) = – 10,000
= $1,095

46. Net Present Value Profile
Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
3,500
( )
3,500
(1+ .15)2
3,500
( )3
3,500
(1+ .15)4
NPV(15%) = – 10,000
= – $7.58

47. Net Present Value Profile
Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
3,500
( )
3,500
(1+ .20)2
3,500
( )3
3,500
(1+ .20)4
NPV(20%) = – 10,000
= – $939

48. Net Present Value Profile
Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
Connect the Points

49. Net Present Value Profile
Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
6,000 N P V
3,000
Cost of Capital 5%
10%
15%
20%
500
(1+ 0 )
500
(1+ 0)2
4,600
(1+ 0 )3
10,000
(1+ 0)4
NPV(0%) = – 10,000
= $5,600

50. Net Present Value Profile
Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
6,000 N P V
3,000
Cost of Capital 5%
10%
15%
20%
500
(1+.05)
500
(1+.05)2
4,600
(1+ .05)3
10,000
(1+ .05)4
NPV(5%) = – 10,000
= $3,130

51. Net Present Value Profile
Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
6,000 N P V
3,000
Cost of Capital 5%
10%
15%
20%
500
(1+.10)
500
(1+.10)2
4,600
(1+ .10)3
10,000
(1+ .10)4
NPV(10%) = – 10,000
= $1.154

52. Net Present Value Profile
Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
6,000 N P V
3,000
Cost of Capital 5%
10%
15%
20%
500
(1+.15)
500
(1+.15)2
4,600
(1+ .15)3
10,000
(1+ .15)4
NPV(15%) = – 10,000
= –$445

53. Net Present Value Profile
Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
Project B
Connect the Points

54. Net Present Value Profile
Graphs the Net Present Value of the project with different required rates
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
Project B

55. Net Present Value Profile
Compare NPV of the two projects for different required rates
Crossover point
6,000 N P V
Project B
3,000
Project A
Cost of Capital 5%
10%
15%
20%

56. Net Present Value Profile
Compare NPV of the two projects for different required rates
Crossover point
6,000 N P V
Project B
3,000
For any discount rate < crossover point choose B
Project A
Cost of Capital 5%
10%
15%
20%

57. Net Present Value Profile
Compare NPV of the two projects for different required rates
Crossover point
6,000 N P V
Project B
For any discount rate > crossover point choose A
3,000
For any discount rate < crossover point choose B
Project A
Cost of Capital 5%
10%
15%
20%

58. Capital Budgeting Methods
Internal Rate of Return
Measures the rate of return that will make the PV of future CF equal to the initial outlay.
Definition:
The IRR is that discount rate at which
NPV = 0
IRR is like the YTM. It is the same cocept but the term YTM is used only for bonds.

59. Capital Budgeting Methods
Internal Rate of Return
Measures the rate of return that will make the PV of future CF equal to the initial outlay.
The IRR is the discount rate at which NPV = 0
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
Project B
NPV = $0

60. Capital Budgeting Methods
Internal Rate of Return
Measures the rate of return that will make the PV of future CF equal to the initial outlay.
Or, the IRR is the discount rate at which NPV = 0
6,000 N P V
Project B
3,000
IRRA » 15%
NPV = $0
IRRB » 14%
Cost of Capital 5%
10%
15%
20%

61. Capital Budgeting Methods
Internal Rate of Return
Determine the mathematical solution for IRR

62. Capital Budgeting Methods
Internal Rate of Return
Determine the mathematical solution for IRR
CF1
(1+ IRR )
CF2
(1+ IRR )2
CFn
(1+ IRR )n
0 = NPV = ··· – IO

63. Capital Budgeting Methods
Internal Rate of Return
Determine the mathematical solution for IRR
CF1
(1+ IRR )
CF2
(1+ IRR )2
CFn
(1+ IRR )n
0 = NPV = ··· – IO
CF1
(1+ IRR )
CF2
(1+ IRR )2
CFn
(1+ IRR )n
IO = ···+
Outflow = PV of Inflows

64. Capital Budgeting Methods
Internal Rate of Return
Determine the mathematical solution for IRR
CF1
(1+ IRR )
CF2
(1+ IRR )2
CFn
(1+ IRR )n
0 = NPV = ··· – IO
CF1
(1+ IRR )
CF2
(1+ IRR )2
CFn
(1+ IRR )n
IO = ···+
Outflow = PV of Inflows
Solve for Discount Rates

65. Capital Budgeting Methods
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
Project B
IRRB » 14%
Internal Rate of Return
For Project B
Cannot solve for IRR
directly, must use Trial &
Error
500
(1+ IRR )
500
(1+ IRR )2
4,600
(1+ IRR )3
10,000
(1+ IRR )4
10,000 =

66. Capital Budgeting Methods
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
Project B
IRRB » 14%
Internal Rate of Return
For Project B
Cannot solve for IRR
directly, must use Trial &
Error
500
(1+ IRR )
500
(1+ IRR )2
4,600
(1+ IRR )3
10,000
(1+ IRR )4
10,000 =
TRY 14% ?
500
( )
500
(1+ .14)2
4,600
( )3
10,000
( )4
10,000 =

67. Capital Budgeting Methods
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
Project B
IRRB » 14%
Internal Rate of Return
For Project B
Cannot solve for IRR
directly, must use Trial &
Error
500
(1+ IRR )
500
(1+ IRR )2
4,600
(1+ IRR )3
10,000
(1+ IRR )4
10,000 =
TRY 14% ?
500
( )
500
(1+ .14)2
4,600
( )3
10,000
( )4
10,000 = ?
10,000 = 9,849
PV of Inflows too low, try lower rate

68. Capital Budgeting Methods
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
Project B
IRRB » 14%
Internal Rate of Return
For Project B
Cannot solve for IRR
directly, must use Trial &
Error
500
(1+ IRR )
500
(1+ IRR )2
4,600
(1+ IRR )3
10,000
(1+ IRR )4
10,000 =
TRY 13% ?
500
( )
500
(1+ .13)2
4,600
( )3
10,000
( )4
10,000 =

69. Capital Budgeting Methods
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
Project B
IRRB » 14%
Internal Rate of Return
For Project B
Cannot solve for IRR
directly, must use Trial &
Error
500
(1+ IRR )
500
(1+ IRR )2
4,600
(1+ IRR )3
10,000
(1+ IRR )4
10,000 =
TRY 13% ?
500
( )
500
(1+ .13)2
4,600
( )3
10,000
( )4
10,000 = ?
10,000 = 10,155

70. Capital Budgeting Methods
10% 5%
Cost of Capital N P V
6,000
3,000
20%
15%
Project B
IRRB » 14%
Internal Rate of Return
For Project B
Cannot solve for IRR
directly, must use Trial &
Error
500
(1+ IRR )
500
(1+ IRR )2
4,600
(1+ IRR )3
10,000
(1+ IRR )4
10,000 =
TRY 13% ?
500
( )
500
(1+ .13)2
4,600
( )3
10,000
( )4
10,000 = ?
10,000 = 10,155
13% < IRR < 14%

71. Capital Budgeting Methods
Decision Rule for Internal Rate of Return
Independent Projects
Accept Projects with
IRR ³ required rate
Mutually Exclusive Projects
Accept project with highest

72. Capital Budgeting Methods
Profitability Index
Very Similar to Net Present Value
PV of Inflows
Initial Outlay
PI =

73. Capital Budgeting Methods
Profitability Index
Very Similar to Net Present Value
PV of Inflows
Initial Outlay
PI =
Instead of Subtracting the Initial Outlay from the PV
of Inflows, the Profitability Index is the ratio of Initial
Outlay to the PV of Inflows.

74. Capital Budgeting Methods
Profitability Index
Very Similar to Net Present Value
PV of Inflows
Initial Outlay
PI =
Instead of Subtracting the Initial Outlay from the PV
of Inflows, the Profitability Index is the ratio of Initial
Outlay to the PV of Inflows.
CF1
(1+ k )
CF2
(1+ k )2
CF3
(1+ k )3
CFn
(1+ k )n
···+
PI = IO

75. Capital Budgeting Methods
Profitability Index for Project B
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
500
(1+ .1 )
(1+ .1)2
4,600
(1+ .1 )3
10,000
(1+ .1 )4
PI =
10,000

76. Capital Budgeting Methods
Profitability Index for Project B
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
500
(1+ .1 )
(1+ .1)2
4,600
(1+ .1 )3
10,000
(1+ .1 )4
PI =
10,000
11,154
10,000
PI = =

77. Capital Budgeting Methods
Profitability Index for Project B
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
500
(1+ .1 )
(1+ .1)2
4,600
(1+ .1 )3
10,000
(1+ .1 )4
PI =
10,000
11,154
10,000
PI = =
Profitability Index for Project A
3,500 x PVIFA 4, .10
PI =
10,000

78. Capital Budgeting Methods
Profitability Index for Project B
P R O J E C T
Time A B
0 (10,000.) (10,000.)
1 3,
2 3,
3 3,500 4,600
4 3,500 10,000
500
(1+ .1 )
(1+ .1)2
4,600
(1+ .1 )3
10,000
(1+ .1 )4
PI =
10,000
11,154
10,000
PI = =
Profitability Index for Project A 1
.10 1
.10(1+.10)4
3,500( )
PI =
10,000
11,095
10,000
PI = =

79. Capital Budgeting Methods
Profitability Index Decision Rules
Independent Projects
Accept Project if PI ³ 1
Mutually Exclusive Projects
Accept Highest PI ³ 1 Project

80. Comparison of Methods Project A Project B Choose
Payback < 3 years < 4 years A
NPV $1,095 $1,154 B
IRR 14.96% 13.50% A
PI B

81. Comparison of Methods Time Value of Money
Payback - Does not adjust for timing differences (ignore Discounted Payback)
NPV, IRR and PI take into account the time value of money

82. Comparison of Methods Time Value of Money Relevant Cash Flows?
Payback - Does not adjust for timing differences
NPV, IRR and PI take into account the time value of money
Relevant Cash Flows?
NPV, IRR and PI use all Cash Flows
Payback method ignores Cash Flows that occur after the Payback Period.

83. Comparison of Methods Time Value of Money Relevant Cash Flows?
Payback - Does not adjust for timing differences
NPV, IRR and PI take into account the time value of money
Relevant Cash Flows?
NPV, IRR and PI use all Cash Flows
Payback method ignores Cash Flows that occur after the Payback Period.
Project 1
(10,000)
5,000
5,000

84. Comparison of Methods Time Value of Money Relevant Cash Flows?
Payback - Does not adjust for timing differences
NPV, IRR and PI take into account the time value of money
Relevant Cash Flows?
NPV, IRR and PI use all Cash Flows
Payback method ignores Cash Flows that occur after the Payback Period.
Project 1
Both Projects have
Identical Payback
(10,000)
5,000
5,000
Project 2
(10,000)
5,000
5,000
10,000

85. Comparison of Methods
NPV & PI indicated accept Project B while IRR indicated that Project A should be accepted. Why?
Sometimes there is a conflict between the decisions based on NPV and IRR methods.
The conflict arises if there is difference in the timing of CFs or sizes of the projects (or both).
The cause of the conflict is the underlying reinvestment rate assumption.
Reinvestment Rate Assumptions
NPV assumes cash flows are reinvested at the required rate, k.
IRR assumes cash flows are reinvested at IRR.
Reinvestment Rate of k more realistic as most projects earn approximately k (due to competition)
NPV is the Better Method for project evaluation

86. IRR
Because of its unreasonable reinvestment rate assumption, IRR method can result in bad decisions. Another problem with IRR is that if the sign of the cash flow changes more than once, there is a possibility of multiple IRR. See p 340.
The problem of unreasonable assumption can be addressed by using Modified IRR

87. MIRR
To find MIRR
1.Find the FV of all intermediate CFs using the cost of capital (the hurdle rate) as the interest rate.
2.Add all FV.
3. Find that discount rate which makes the PV of the FV equal to the PV of outflows.
Drop MIRR computations.